Find the interest and the amount on:

₹ 5,000 at 8% per year from 23rd December 2011 to 29th July 2012.

Given:

P = ₹ 5,000

R = 8%

To calculate time (T):

Dec = 8 days (31 - 23)

Jan = 31 days

Feb = 29 days

March = 31 days

April = 30 days

May = 31 days

June = 30 days

July = 29 days

Total = 219 days

T = 219 days

= $\Big(\dfrac{219}{365}\Big)$ years

= $\Big(\dfrac{3}{5}\Big)$ years

$\because \text{S.I.} = ₹ \Big(\dfrac{P \times R \times T}{100}\Big)\\[1em] \Rightarrow \text{S.I.} = ₹ \Big(\dfrac{5,000 \times 8 \times 3}{5 \times 100}\Big)\\[1em] \Rightarrow \text{S.I.} = ₹ \dfrac{1,20,000}{500}\\[1em] \Rightarrow \text{S.I.} = ₹ 240 \\[2em] \because \text{A = P + S.I.}\\[1em] \Rightarrow \text{A = ₹ 5,000 + ₹ 240}\\[1em] \Rightarrow \text{A = ₹ 5,240}\\[1em]$

Hence, S.I. = ₹ 240 and Amount = ₹ 5,240.